Coordinate planes are two-dimensional planes formed by the intersection of a vertical line known as the y-axis and a horizontal line known as the x-axis. Lines intersecting at zero are called perpendicular lines, and this is the origin.
Table of Contents
What is a Coordinate Plane?
Coordinate planes are two-dimensional surfaces formed by two number lines. It is formed when a horizontal line called the X-axis and a vertical line called the Y-axis to intersect at a point called the origin. To locate points on a coordinate grid, numbers are used. Coordinate planes can be used to graph points, lines, and much more. It provides precise directions from one point to another and acts as a map.
Coordinate Plane Definition
A coordinate plane, also known as a rectangular coordinate plane grid, is a two-dimensional plane formed by the intersection of a vertical axis and a horizontal axis.
Coordinate Plane Graph
There are two perpendicular number lines called axes in a coordinate graph, which is sometimes called a coordinate plane.
Coordinates are two numbers that determine a specific position on a coordinate plane, also known as a coordinate grid. A point in a coordinate plane is named by its ordered pair (x, y) written in parentheses, which corresponds to the X-coordinate and the Y-coordinate. Depending on the location of the point in the quadrant, these coordinates can be positive, zero, or negative.
Quadrants on a Coordinate Plane
Quadrants are regions or parts of a cartesian or coordinate plane formed when two axes intersect.
- First quadrant: x > 0, y > 0
- Second quadrant: x < 0, y > 0
- Third quadrant: x < 0, y < 0
- Fourth quadrant: x > 0, y < 0
Locating a Point on the Coordinate Plane
Let us now discuss how to identify points on a coordinate plane, since we are already familiar with the coordinate plane and its parts. You can locate a point on the coordinate plane by following these steps:
- Step 1: Locate the point.
- Step 2: Determine the quadrant by looking at its X and Y coordinates.
- Step 3: Determine the X-coordinate or abscissa of the point by reading the number of units to the right/left of the origin along the X-axis.
- Step 4: Determine the Y-coordinate or the ordinate of the point by reading the number of units the point is above/below the origin along the Y-axis.
Let’s look at the coordinate plane examples. Look at the figure shown below.
- Step 1: Look at the blue dot on the coordinate graph.
- Step 2: It is in the second quadrant.
- Step 3: Along the negative X-axis, the point is 3 units away from the origin.
- Step 4: The point is 2 units away from the origin along the positive Y-axis.
Thus, the point on the graph has coordinates (-3, 2).
Plotting a Point in the Coordinate Plane
In this section, we are about to learn how to plot a point on the coordinate plane. Let’s take the example of point P = (5, 6). Follow the steps below to plot a point in the coordinate plane:
- Step 1: Draw two perpendiculars, the X-axis and the Y-axis.
- Step 2: Start from the origin. Move 5 units to the right, along the positive X-axis.
- Step 3: Move 6 units up, along the positive Y-axis.
- Step 4: Mark the point of intersection. Mark it as (5, 6).
Note that P is in the first quadrant. The positive coordinate plane is also known as the positive coordinate plane because the coordinates for any point in this quadrant will be positive.
Key Points on the Coordinate Plane:
- The first quadrant (+, +) known as the positive coordinates quadrant, is denoted by the Roman numeral I.
- The second quadrant (-, +) is denoted by the Roman numeral II.
- The third quadrant (-, -) is represented by the Roman numeral III.
- The fourth quadrant (+, -) is represented by the Roman numeral IV.
- The coordinates of any point are enclosed in brackets.
A coordinate plane is a two-dimensional plane formed by the intersection of the x-axis, or the horizontal line, and the y-axis, or the vertical line. They intersect at a point known as the origin, where the perpendicular lines cross.
This coordinate system was invented in the 17th century by French mathematician René Descartes.
The coordinate plane contains the axes (X-axis and Y-axis), the origin (0,0), and the four quadrants.
Coordinate planes have their origin at the point of intersection of two axes. 0 and 0 are the coordinates for the origin.
The following steps can be taken to construct a coordinate plane:
Take a sheet of graph or grid paper.
Draw a horizontal line. As the x-axis locates values of x, this line is known as the x-axis.
Draw a vertical line. This line is called the y-axis and is used to locate values of y. To show that the axis actually
Note: To demonstrate that the axes actually continue forever in both directions, use arrowheads at each end.
Cartesian coordinates work well with so many situations in real life, such as when deciding how furniture should be placed in a room, a two-dimensional grid can be drawn representing the room and thus the appropriate unit of measurement can be chosen.
Coordinates can be used to graph any point or object. You can plot the coordinates of given points in each quadrant of the coordinate plane and join them to form a particular shape or object.
There are four quadrants in a coordinate plane. There are four quadrants, which are denoted by the Roman numerals I, II, III, and IV, depending on the sign of the coordinates.
We can read the coordinate plane in the following way:
Determine the quadrant in which the given point is located by looking at its x and y coordinates.
Read the number of units the point is to the right/left of the origin along the x-axis to determine its x coordinate.
Read the number of units the point is on the upward/downward side of the origin along the y-axis to find its y coordinate.
The different types of lines in a coordinate plane are parallel lines, intersecting lines, skew lines, coplanar lines, coincident lines. All of these lines can be drawn in the coordinate plane based on the x, y, and z axes.